19. Fluid Mechanics

(II) A spherical balloon has a radius of 7.15 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 890 kg? Neglect the buoyant force on the cargo volume itself.

When an object of unknown mass and volume is fully immersed in large oil (800 kg/m³ ) container and released from rest, it stays at rest. Calculate the density of this object.

If your average density is $\rho$ and you are floating gently in freshwater with density $1000kg/m^3$, what fraction of your volume will be submerged?

Which of the following best explains Archimedes' principle?

Calculate the true mass (in vacuum) of an aluminum sphere whose apparent mass is 4.0000 kg when weighed in air.

In FIGURE CP14.74, a cone of density ρ₀ and total height l floats in a liquid of density ρ_f. The height of the cone above the liquid is h. What is the ratio h/l of the exposed height to the total height?

A submarine is stranded on the bottom of the ocean. Which of the following statements best explains why the buoyant force acting on the submarine does not cause it to rise to the surface?

A simple model (Fig. 13–62) considers a continent as a block ( density ≈ 2800 kg/m³) floating in the mantle rock around it ( density ≈ 3300 kg/m³). Assuming the continent is 35 km thick (the average thickness of the Earth’s continental crust), estimate the height of the continent above the surrounding mantle rock.

How many helium-filled balloons would it take to lift a person? Assume the person has a mass of 72 kg and that each helium-filled balloon is spherical with a diameter of 36 cm.

Why does a hot air balloon rise in the atmosphere?

What is the tension of the string in FIGURE EX14.19?

If the entire apparatus is completely submerged in water, which of the following statements about the buoyant force acting on it is correct?

A raft is made of 12 logs lashed together. Each is 45 cm in diameter and has a length of 6.5 m. How many people can the raft hold before they start getting their feet wet, assuming the average person has a mass of 68 kg? Do not neglect the weight of the logs. Assume the specific gravity of wood is 0.60.

A cubical block of wood, 10.0 cm on a side, floats at the interface between oil and water with its lower surface 1.50 cm below the interface (Fig. E12.33). The density of the oil is 790 kg/m³. (a) What is the gauge pressure at the upper face of the block? (b) What is the gauge pressure at the lower face of the block?